Electricity Market Modelling€¦ · Electricity Market Modelling Economic Dispatch and...

Electricity Market Modelling

Economic Dispatch and Hydro-thermal Scheduling

Tony Downward

Energy Centre / Electric Power Optimization Centre

Energy Centre Summer School 2020, University of Auckland.

Outline

Capacity Investment

Generation Technologies

Load Profile

Load Duration & Screening Curves

Economic Dispatch & Pricing

Wholesale Market

Transmission

River-chains & Hydro-storage

Hydro Resources

Hydro Risk Curves

Hydro-thermal Scheduling

Outline

Capacity Investment

Load Profile

Wholesale Market

Transmission

Hydro Resources

Hydro Risk Curves

Capacity InvestmentLoad Profile

The load profile is cyclical:

– Daily cycles: morning and evening peaks.– Weekly cycles: lowest usage during weekends.– Yearly cycles: additional power usage during winter for lighting/heating. (In someplaces, summer demand may increase due to air conditioning).

Load Profile• The load profile is cyclical:

– Daily cycles: morning and evening peaks.– Weekly cycles: lowest usage during weekends.– Yearly cycles: additional power usage during winter for

lighting/heating. (In some places summer may increase air conditioning).

Capacity InvestmentLoad Duration Curve

If we sort observed loads from highest to lowest we can construct a load-duration curvewhich specifies how often the load exceeds a certain value.

Load Duration Curve• If we sort observed loads from highest to lowest we can

construct a load-duration curve which specified how often the load exceeds a certain value.

Capacity InvestmentLoad Duration Curve

If we sort observed loads from highest to lowest we can construct a load-duration curvewhich specifies how often the load exceeds a certain value.

Load Duration Curve• If we sort observed loads from highest to lowest we can

construct a load-duration curve which specified how often the load exceeds a certain value.

Baseload (Coal, Hydro)

Peakers (OCGT)

Capacity InvestmentScreening Curve

To procure the most cost effective mix of generation, a central planner would usescreening curves. These would display the cost of generation as a function of totaloperating hours for each technology.

Screening curves

To procure the most cost effective mix of generation, a centralplanner would use screening curves. These would display the costof generation as a function of total operating hours for eachtechnology.

Golbon Zakeri Energy CentreUoA2019

Energy 721 – Electricity section

Outline

Capacity Investment

Load Profile

Wholesale Market

Transmission

Hydro Resources

Hydro Risk Curves

Economic Dispatch & PricingWholesale Market Overview

In New Zealand, all power is traded in a real-time wholesale market.

Bids are locked-in prior to dispatch.

Each plant can offer a five-tranche offer-stack.

Retailers or large industrials may submit bids.

Transpower (the system operator) accepts power from plants so as to minimize thecost, while complying with the constraints imposed by the transmission grid.

Economic Dispatch & PricingSingle-node Dispatch

Given the following offers:

– 100MW @ $10 (Hydro)– 300MW @ $40 (CCGT)– 200MW @ $60 (OCGT)– 100MW @ $0 (Wind)

What is the optimal dispatch, if the demand is(a) 450MW, (b) 550MW?

How much should consumers pay for the power?

Single-Node Dispatch• For a single-node, it is clear how the system operator

should decide who to dispatch.

SupplyDemandP

Market clearing price System MC

Covers FC

Hydrocoal

Old GTs

Economic Dispatch & PricingTransmission

An electricity transmission network consists of buses (nodes) and lines.

The buses are either grid exit points, GXPs (where power is taken off the grid), or gridinjection points.

The transmission lines carry power from the node where it’s generated to the nodewhere the power is taken off the grid and distributed to consumers.

Transmission lines have three important properties:

– thermal capacity (maximum amount of power that can be send);– resistance (affects the power loss over a transmission line); and– impedance / reactance (governs how power flows through the network).

Economic Dispatch & PricingTransmission

An electricity transmission network consists of buses (nodes) and lines.

The buses are either grid exit points, GXPs (where power is taken off the grid), or gridinjection points.

The transmission lines carry power from the node where it’s generated to the nodewhere the power is taken off the grid and distributed to consumers.

Transmission lines have three important properties:

– thermal capacity (maximum amount of power that can be send);– resistance (affects the power loss over a transmission line); and– impedance / reactance (governs how power flows through the network).

Economic Dispatch & PricingDC load flow approximation

The electricity grid is truly an AC system; finding the optimal power flow involvessolving a highly non-linear and non-convex system of equations.

Approximations can be made, reducing this to a linear system.

This approximation has the following constraints:

– node-balance (generation + inflows = load + outflows);– loop flow (Kirchhoff’s law); and– flows must comply with thermal limits.

Economic Dispatch & PricingDC load flow approximation

The electricity grid is truly an AC system; finding the optimal power flow involvessolving a highly non-linear and non-convex system of equations.

Approximations can be made, reducing this to a linear system.

This approximation has the following constraints:

– node-balance (generation + inflows = load + outflows);– loop flow (Kirchhoff’s law); and– flows must comply with thermal limits.

DC load-flow approximation

• Node-balance constraint: Mq + Af = d

• Loop-flow constraint: Lf = 0

• Thermal limits: | f | ≤ K

50MW 150MW

• Node-balance constraints

100 – f12 – f13 = 0

50 – f23 + f12 = 0

f13 + f23 = 150

50MW 150MW

16.7MW

66.7MW

83.3MW

• Loop-flow constraint

x12 f12 – x13 f13 + x23 f23 = 0

50MW 150MW

Economic Dispatch Problem

• Originally devised by Schweppe et al. in the early 1980s.

• Further developed by Hogan in a series of papers in the late 80s and early 90s.

min cTq

s/t Mq + Af – 1/2rf 2 = d [π]

Lf = 0

| f | ≤ K

0 ≤ q ≤ Q

Economic Dispatch Problem

• Given offer stacks from generators, the system operator chooses generation levels for each generator so as to minimize the total cost of dispatch, subject to satisfying demand and all physical constraints.

• Set price equal to the shadow price of electricity at each node (this is the marginal cost of supplying an additional unit of electricity at that node).

Power Exchange Market

Demand = 80MW

(100MW @ $60/MW)

(100MW @ $40/MW)

No Network Constraints

Demand = 80MW

(80MW)

LOWEST COST DISPATCH = 80 × $40 =

$40 $40

No Network Constraints

Demand = 80MW

(100MW @ $60/MW)

(100MW @ $40/MW)

MAX: 40MW

With Network Constraints

Demand = 80MW

(40MW)

NEW LOWEST COST DISPATCH = 40 × $40 + 40 ×

$60 = $4000

$40 $60

(40MW)

With Network Constraints

Demand = 100MW

(100MW)

With Loop Flows

Demand = 100MW

(100MW)

With Loop Flows

Demand = 200MW

(100MW)

With Loop Flows

MAX: 20MW

Demand = 80MW

(100MW @ $40/MW)

(100MW @ $60/MW)

With Loop Flows

Demand = 80MW

(70MW)

(10MW)

46.67 + 3.33

23.33 – 3.33 23.33 + 6.67

LOWEST COST DISPATCH = 70 × $40 + 10 × $60 =

$40 $50

With Loop Flows

Outline

Capacity Investment

Load Profile

Wholesale Market

Transmission

Hydro Resources

Hydro Risk Curves

River Chains / StorageSummary of Resources

Hydro Scheme Capacity # Reservoirs # Stations OwnerWaikato 1,050 MW 8 9 MercuryTongariro 360 MW 1 2 GenesisTekapo 185 MW 1 2 GenesisWaitaki 1,550 MW 6 6 MeridianClutha 760 MW 2 2 ContactManapouri 850 MW 1 1 Meridian

River Chains & Hydro-storageWaitaki System

Google Maps

River Chains & Hydro-storageTime-scales

Within a river chain there are a number of interconnected reservoirs. Some of thereservoirs are large with, weeks of storage, whereas others may have less than a day ofstorage. Therefore these electricity generators need to manage their water overmultiple time-scales.

I Hourly: ensure that generators are operating at efficient levels, and the plants areready to respond to contingency events (reserve).

I Daily: ensure that water is positioned correctly within the river chain so thatmaximum generation can be achieved during peak periods.

I Seasonally: ensure that the overall amount of water in the reservoirs is sufficientto meet future demand.

For all of these time-scales, the key risks are that water could get spilled or that areservoir becomes effectively empty.

River Chains & Hydro-storageJADE model of River Chains

JADE model network.

River Chains & Hydro-storageHydro Risk Curves

NZ Controlled Storage and Risk Curve

Mean NZ Storage Nominal NZ Full Controlled Storage 1% Risk 2% Risk

4% Risk 6% Risk 8% Risk Emergency Zone

Nominal NZ Full (Lakes Taupo, Tekapo, Pukaki, Hawea, Te Anau & Manapouri)

Updated 17 Feb 2019

Transpower NZ

River Chains & Hydro-storageSimulated Trajectories

rage G

NZ Actual Controlled Storage and Risk Curve

Nominal NZ Full Actual Storage 1% Risk 4% Risk Emergency Zone

Update: 11th December 2018

Nominal NZ full

(Projected range of

storage scenarios)

(Lakes Taupo, Tekapo, Pukaki, Hawea, Te Anau & Manapouri)

Actual storage courtesy of NZX Hydro

Transpower NZ

River Chains & Hydro-storageHydro-thermal Scheduling

In a system with a a significant proportion of hydro-electric generation, such as NewZealand, it is critical to manage the storage carefully. This is done through watervaluation.

Put simply, we should value water at the opportunity cost of water in future periods.Let us first consider two extreme situations.

– What should the value of water be if the reservoir is full?

– What should the value of water be if the reservoir is empty?

It is non-trivial to estimate the water value for any other reservoir levels, since this willdepend on: the time of year, projected future inflows, costs of other plants or demandresponse, etc.

Hydro-thermal SchedulingStylised Example

Consider a single-node system, with three generators

– a hydro plant (500MW);– a gas plant (400MW, w/ SRMC: $60/MWh); and– a coal plant (250MW, SRMC: $80/MWh), and a VOLL of $1000/MWh.

Suppose we consider two periods (each one-hour long) with a constant demand of1000MW.

– What should we do if we start with 1300MWh? What is the water value?

Hydro-thermal SchedulingMore Realistic Scenario

In reality, future inflows are random, so we cannot be sure how much water we willhave in the future, so we must consider the expected (average) opportunity cost,associated with using water now.

Typically, these models are run over a year, with a weekly time-step.

Figure 5.3 shows the convergence of the terminal marginal water value for the currentscenario of the NZEM. Note how in the legend that Iterations 14 and 15 are coloured blue andred respectively but in Figure 5.3 a pink line is seen. This means the lines are directly on topof one another and the 1D approximation of the marginal water values are identical (implyingconvergence) for iterations 14 and 15.

500 1,000 1,500 2,000 2,500 3,000 3,500 4,000

x, GWh

alue, $

Figure 5.3: Plot of convergence of terminal marginal water value, V ′T (x)

The convergence of this criterion implies that the policy of the of the problem has converged.This is because the marginal water values for a given set of reservoir levels informs the hydro-thermal scheduling decision.

To summarise this section so far of all three criteria have converged. The convergence ofthese criteria implies convergence of the infinite-horizon SDDP algorithm. The rest of thisSection discusses how variation of the user chosen parameter J , (insignificantly) affects ourthree convergence criteria.

5.4 Expected Terminal Future Cost-To-Go Update Frequency

We chose to cache stage 1 cuts for 500 iterations of SDDP before determining the δ̂ to shiftthe new stage 1 cuts down by (then update VT+1(x). As J is the number of iterations ofSDDP to run per ‘outer loop’ this means we have been setting J = 500. This choice for J waschosen from the supervisor of this project’s specialised knowledge of JADE and SDDP. Choicessuch as caching the stage 1 cuts for 200 or 1000 iterations of SDDP (or anything in-between)before determining the δ̂ may result in faster convergence of δ̂ → ∆. Inspection on how theconvergence of the other two criteria with the different choices of J is also of interest.

The infinite-horizon model was run with J = 100, 200, 320, 400, 500, 615, 800, and 1000.The total number of iterations pf SDDP was kept constant at 8000 iterations. Hence the numberof iterations of the outer loop (I) also varied.

5.4.1 Terminal Future Expected Cost-To-Go Integral Convergence

The terminal cost integral converged for all cases. Recall from 5.2 that this implies the expectedfuture terminal cost-to-go function has converged. However, the value of the terminal marginalintegral for each case was different. This was expected because of initial (bad) values for δ̂ishift the expected future terminal cost-to-go function to different heights.

Summary

Mathematical modelling and optimisation is used throughout the planning andoperations of electricity systems.

It order to make the right decisions, we need to consider both long-, medium- andshort-term uncertainties, around demand, and hydrology.

This afternoon, we will run interactive simulations of the economic dispatch model,and also consider hydro storage. These simulations will be in Labs 8 and 9 on Level 0,OGGB.

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